Illustrative Mathematics Unit 6.7, Lesson 6: Absolute Value of Numbers

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Illustrative Math
Grade 6

Lesson 6: Absolute Value of Numbers

Let’s explore distances from zero more closely.

Illustrative Math Unit 6.7, Lesson 6 (printable worksheets)

Lesson 6 Summary

We compare numbers by comparing their positions on the number line: the one farther to the right is greater; the one farther to the left is less.
Sometimes we wish to compare which one is closer to or farther from 0. For example, we may want to know how far away the temperature is from the freezing point of 0°C, regardless of whether it is above or below freezing.
The following diagram gives some examples of absolute value numbers

Lesson 6.1 Number Talk: Closer to Zero

For each pair of expressions, decide mentally which one has a value that is closer to 0.
9/11 or 15/11
1/5 or 1/9
1.25 or 5/4
0.01 or 0.001

• See Video for Whole Lesson

Scroll down the page for the solutions to the “Are you ready for more?” section.

Lesson 6.2 Jumping Flea

Move the bug to a starting point, choose a jump distance, and press the jump button. You may need to zoom in or out if your bug jumps off the screen.
Open Applet

1. A bug is jumping around on a number line.
   a. If the bug starts at 1 and jumps 4 units to the right, where does it end up? How far away from 0 is this?
   b. If the bug starts at 1 and jumps 4 units to the left, where does it end up? How far away from 0 is this?
   c. If the bug starts at 0 and jumps 3 units away, where might it land?
   d. If the bug jumps 7 units and lands at 0, where could it have started?
   e. The absolute value of a number is the distance it is from 0. The bug is currently to the left of 0 and the absolute value of its location is 4. Where on the number line is it?
   f. If the bug is to the left of 0 and the absolute value of its location is 5, where on the number line is it?
   g. If the bug is to the right of 0 and the absolute value of its location is 2.5, where on the number line is it?
   
2. We use the notation |-2| to say “the absolute value of -2,” which means “the distance of -2 from 0 on the number line.”
   a. What does |-7| mean and what is its value?
   b. What does |1.8| mean and what is its value?
   
3. For another challenge, show a target and move it wherever you want it. Can you set the jump to land on it?
   

Lesson 6.3 Absolute Elevation and Temperature

1. A part of the city of New Orleans is 6 feet below sea level. We can use “-6 feet” to describe its elevation, and “|-6| feet” to describe its vertical distance from sea level. In the context of elevation, what would each of the following numbers describe?
   a. 25 feet
   b. |25| feet
   c. -8 feet
   d. |-8| feet
   
2. The elevation of a city is different from sea level by 10 feet. Name the two elevations that the city could have.
   
3. We write “-5°C” to describe a temperature that is 5 degrees Celsius below freezing point and “5°C” for a temperature that is 5 degrees above freezing. In this context, what do each of the following numbers describe?
   a. 1°C
   b. -4°C
   c. |12|°C
   d. |-7|°C
   
4. a.Which temperature is colder: -6°C or 3°C?
   b. Which temperature is closer to freezing temperature: -6°C or 3°C?
   c. Which temperature has a smaller absolute value? Explain how you know.
   
   

Are you ready for more?

At a certain time, the difference between the temperature in New York City and in Boston was 7 degrees Celsius. The difference between the temperature in Boston and in Chicago was also 7 degrees Celsius. Was the temperature in New York City the same as the temperature in Chicago? Explain your answer.

• Show Answers

  Not necessarily. The temperature at New York City could be 7 degrees hotter than Boston while the temperature at Chicago could be 7 degrees colder than Boston or vice versa.

Lesson 6 Practice Problems

1. On the number line, plot and label all numbers with an absolute value of 3/2.
   
2. The temperature at dawn is 6°C away from 0. Select all the temperatures that are possible.
   A. -12°C
   B. -6°C
   C. 0°C
   D. 6°C
   E. 12°C
   
3. Order from least to greatest:
   |-2.7|
   0
   1.3
   |-1|
   2
   
4. Elena donates some money to charity whenever she earns money as a babysitter. The table shows how much money, d, she donates for different amounts of money, m, that she earns.
   

d	4.44	1.80	3.12	3.60	2.16
m	37	15	26	30	18

a. What percent of her income does Elena donate to charity? Explain or show your work.
b. Which quantity, m or d, would be the better choice for the dependent variable in an equation describing the relationship between m and d? Explain your reasoning.
Use your choice from the second question to write an equation that relates m and d.
5. How many times larger is the first number in the pair than the second?
a. 3⁴ is _____ times larger than 3³.
b. 5³ is _____ times larger than 5².
c. 7¹⁰ is _____ times larger than 7⁸.
d. 17⁶ is _____ times larger than 17⁴.
e. 5¹⁰ is _____ times larger than 5⁴.
6. Lin’s family needs to travel 325 miles to reach her grandmother’s house.
a. At 26 miles, what percentage of the trip’s distance have they completed?
b. How far have they traveled when they have completed 72% of the trip’s distance?
c. At 377 miles, what percentage of the trip’s distance have they completed?

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